Generalized Fuzzy Numbers Comparison by Geometric Moments

-In the field of engineering and economic studies, mathematical manipulation of fuzzy numbers is cumbersome and does not provide a neatly ordered set of results in the same way that crisp numbers do. Moreover, the generalized fuzzy number (i.e. non-normalized and normalized fuzzy number) have been approved more flexible and more intelligent than the normalized fuzzy number since it takes the degree of confidence of the decision-makers’ opinions into account. In this paper the concept of the probability measure of fuzzy events is used to represent the fuzzy alternatives, and a ranking approach based upon their geometric moments are developed to make decision. The approach is computationally simple and its underlying concepts are logically sound. A fuzzy number with a superior geometric mean is ranked above fuzzy numbers having inferior geometric means, and in the case where the geometric means of two numbers happen to be equal, the number with a lower geometric variance is ranked above fuzzy numbers whose geometric variances are higher. A comparative study is conducted on cases used in the previous literatures to examine the performance of the proposed method on rationality and discriminatory ability. Key-words: Decision-making, Probabilistic moments, Fuzzy number, Mellin transform.